In this example, we will solve the 1D heat equation
$\dfrac{\partial T}{\partial t} = \kappa \dfrac{\partial^2 T}{\partial x^2}$, with $\kappa = 1$
subject to the following boundary conditions:
$\Delta t=\nu \dfrac{\Delta x^2}{2 \kappa}$, where $\nu \leq 1$ is the Courant number.
In the figures below, we vary $\Delta t$ and $\Delta x$ to see the effect on the solution.
Use the sliders to determine which values of $\Delta t$ and $\Delta x$ lead to stable solutions.